The angles of a triangle are in A.P., and the number of degrees in the

1.	The angles of a triangle are in A.P., and the number of degrees in the least angle is to the number of degrees in the mean angle as 1:120. Find the angle in radians.
Answer» Suppose the angles of the triangle be (a – d)°, a° and (a + d)°. As we know that, the sum of the angles of a triangle is 180°. a – d + a + a + d = 180° 3a = 180° a = 60° Given as The number of degrees in the least angle/The number of degrees in the mean angle = 1/120 (a - d)/a = 1/120 (60 - d)/60 = 1/120 (60 - d)/1 = 1/2 120 - 2d = 1 2d = 119 d = 119/2 = 59.5 ∴ The angles are: (a – d)° = 60° – 59.5° = 0.5° a° = 60° (a + d)° = 60° + 59.5° = 119.5° The angles of triangle in radians (0.5 × π/180) rad = π/360 (60 × π/180) rad = π/3 (119.5 × π/180) rad = 239π/360

The angles of a triangle are in A.P., and the number of degrees in the least angle is to the number of degrees in the mean angle as 1:120. Find the angle in radians.

Answer»

Suppose the angles of the triangle be (a – d)°, a° and (a + d)°.

As we know that, the sum of the angles of a triangle is 180°.

a – d + a + a + d = 180°

3a = 180°

a = 60°

Given as

The number of degrees in the least angle/The number of degrees in the mean angle = 1/120

(a - d)/a = 1/120
(60 - d)/60 = 1/120

(60 - d)/1 = 1/2

120 - 2d = 1
2d = 119

d = 119/2

= 59.5

∴ The angles are:

(a – d)° = 60° – 59.5° = 0.5°

a° = 60°

(a + d)° = 60° + 59.5° = 119.5°

The angles of triangle in radians

(0.5 × π/180) rad = π/360

(60 × π/180) rad = π/3

(119.5 × π/180) rad = 239π/360